Arnaud's 5x5x5 Edge-Pairing method: Examples

[AvGalen]

I thought it would be a good idea to demonstrate how I solve the edges on the 5x5x5. I think this method is at least as fast as the bigcubes.com method. I average around 60 seconds with the "advanced" variation of my method.

The basic idea is to use the 2-at-a-time method that is used by a lot of people on the 4x4x4. If you don't know it, I suggest you learn it first from bigcubes.com. For the 5x5x5 you don't match a wing with another wing, but you match a wing with it's center-edge. If a wing is matched with it's center-edge I call this a semi-pair. If you try this method on a 5x5x5 you will see that it works very good sometimes, but very bad other times, especially if you try to use 4-at-a-time or 6-at-a-time. This is because a center-edge has 2 wings. To avoid those problems you start with a semi-pair and keep it there all the time. If a semi-pair is not available directly after doing centers you have to creat one, which is really easy. The way I perform the edge-pairing is that 0. I put the semi-pair on the upper half of the Left-Front tredge-spot. This means my "1st working wing" is in the lower part of the Left-Front tredge-spot.
1. I then put the first edge-center at the Front-Right-spot
2. I then do a d-move to form a semi-pair at the Front-Right-spot. The "2nd working wing" has been moved to the Right-Back-spot
3. I then replace the first edge-center at the Front-Right-spot with the 2nd edge-center.
4. I then do a d-move to form another semi-pair at the Front-Right-spot. The next "1st working wing" is now at Left-Front again.
There are 3 special cases "Parity before the end", "flipped wing", "full 3-cycle" and they can be handled in different ways. Analyze the examples to find out how I do that.

I have developed a scramble that keeps the centers solved, the edges scrambled pretty well and that is easy and fast to execute. To follow my examples you should have a 5x5x5 cube with a "regular" Blue-Orange-Yellow colorscheme. The scramble should be executed with white on top and green on front. DFRBLU are outer face moves, dfrblu are double layer moves. I don't use slice moves at all.

To make it easier to clarify any questions that people might have I will update this first post with general information. I will use the next five posts for the following examples: Beginner, Intermediate, Advanced, Expert, Other additions such as an example with parity and a worse beginning.

OK, lets get started:

Scramble (57 moves in total, but a wrote them in an easy to follow manner)
r U r' U r U2 r'
F' U
l' U2 l U l' U l
L2 R2 F2 B2

r U r' U r U2 r'
F' U
l' U2 l U l' U l
L R' F2 D' B2

r U r' U r U2 r'
F' U
l' U2 l U l' U l

[AvGalen]

Beginner (117 moves used): Pre-setup to Up-Back, put at Front-Right using (F' U2 F) or (R U R')

Red-White: D B2, (F' U2 F)
Green-Red: B, d (R U R') d'

White-Red: U2, (F' U2 F)
White-Green: B, d (F' U2 F) d'

Orange-Yellow: D2 B2, (F' U2 F)
Blue-Yellow: U2, d (R U R') d'

Green-Yellow: U', (R U R')
Yellow-Blue: U2, d (F' U2 F) d'

Green-White: U, (R U R')
Easy piece (will not match yet) Yellow-Green: d (R U R') d' (special case "Parity before the end")

Yellow-Green: U', (R U R')
Red-Yellow: D B2, d (F' U2 F) d'

Blue-Orange: D2 B2, (R U R')
Yellow-Red: U2, d (F' U2 F) d'

Orange-Green: U, (F' U2 F)
Green-Orange: d (F' U2 F) (R U R') d' (special case "flipped wing")
Red-Blue: x' y (special case "full 3-cyle")

Yellow-Orange: D B2, (R U R')
Easy piece (will not match yet) Red-Green:U d (F' U2 F) d' (special case "Parity before the end")

White-Orange: B' (F' U2 F)
Red-Green: d (F' U2 F) d'
Orange-Blue: y2 z' (special case "full 3-cycle")

Blue-White: U2 (F' U2 F)
White-Blue: d (F' U2 F) (R U R') d' (special cases "flipped wing" and "full 3-cycle")
Orange-White: (special case "full 3-cycle")

[AvGalen]

Intermediate (86 moves used): Put at Front-Right in few moves

Red-White: F D' F'
Green-Red: B', d R U R' d'

White-Red: U F' U' F
White-Green: B, d F' U2 F d'

Orange-Yellow: B R2
Blue-Yellow: d R U' R' d'

Green-Yellow: R
Yellow-Blue: d F' U F d'

Green-White: F D' F'
Red-Blue: d' F U' F' d (special case "Parity before the end")
Red-Yellow: B, d R U R' d'

Blue-Orange: D R
Yellow-Red: d F' U F d'

Orange-Green: B R2
Green-Orange: d (F' U2 F) (R U R') d' (special case "flipped wing")
Yellow Green x2 (special case "full 3-cycle")

White-Orange: D R
Red-Green: d' L' U L d (special case "Parity before the end")
Orange-Blue: d R' D2 R d'
Yellow Orange: y' x (special case "full 3-cycle")

Blue-White: F D F'
White-Blue: d (F' U2 F) (R U R') d' (special case "flipped wing")
Orange-White: (special case "full 3-cycle")

[AvGalen]

Advanced (75 moves used): Put at Front-Right in fewest moves (4u means the top 4 layers or D y)

Red-White: 4b R' (= F z' R')
Green-Red: d R' D2 R d'

White-Red: B R2
White-Green: d F D F' d'

Orange-Yellow: B' R2
Blue-Yellow: d F' U' F d'

Green-Yellow: U' R'
Yellow-Blue: d F D2 F' d'

Green-White: 4b' R (= F' z R)
Red-Blue: d' F' D F d2 (special case "Parity before the end")
White-Orange: F' U' F d'
Red-Green: z2 (special case "full 3-cycle")

Blue-White: D R
White-Blue: d (F' U2 F) (R U R') d' (special case "flipped wing")
Orange-White: x' (special case "full 3-cycle")

Red-Yellow: B' R2
Blue-Orange: d F' U' F d'

Yellow-Red: R'
Orange-Green: B d R U R' d'

Green-Orange: R 4b' R (= R F' z R)
Yellow-Green: d' L' U2 L (special case "Parity before the end")
Yellow-Orange: d2 R' D2 R d'
Orange-Blue: (special case "full 3-cycle")

[AvGalen]

Expert (73 used): Put at Front-Right in fewest moves (4u means the top 4 layers or Dy), use 4-at-a-time on the final edges

Red-White: 4b R' (= F z' R')
Green-Red: d R' D2 R d'

White-Red: B R2
White-Green: d F D F' d'

Orange-Yellow: B' R2
Blue-Yellow: d F' U' F d'

Green-Yellow: U' R'
Yellow-Blue: d F D2 F' d'

Green-White: 4b' R (= F' z R)
Red-Blue: d' F' D F d2 (special case "Parity before the end")
White-Orange: F' U' F d'
Red-Green: z2 (special case "full 3-cycle")

Blue-White: D R
White-Blue: d (F' U2 F) (R U R') d' (special case "flipped wing")
Orange-White: x' (special case "full 3-cycle")

Red-Yellow: B' R2
Blue-Orange: d F' U' F d'

Yellow-Red + Orange-Green: R' d y
Green-Orange + Yellow-Green: F' U2 F R U R'
Yellow-Orange: y' d2 L' U L
Orange-Blue: d2 F D2 F' d'

I would actually recommend against using this method on this example. As you can see it is pretty difficult to see what is happening and you only save a couple of moves. I just included this to show that it is possible.

[AvGalen]

Reserved room to be used later for parity and other additions.

For now it is important to know that (with an unlikely exception, the single edge flip) you will have 50% chance of no parity and 50% chance of the "edge flip/swap" that is explained on this page. If you get it during the solve (not at the end) you shouldn't use this parity fix! For beginners there is an easier algorith to change that parity into a 3-cycle: (d B2)*5. Again, only use the parity fix at the end of the edge-pairing step!

[AvGalen]

Finally, someone writes a reply

The difference is not just the insertion moves!

For beginner you "pre-setup" at Up-Back, you don't do that for intermediate and further. This saves a lot of moves, but it also means there are a lot more insertion moves. With a bit of practice these insertion moves will be easy and short (intermediate) or even easier and shorter (advanced) if you use some cube rotations/4-layer-turnes.

Another difference are the way you handle (special case "Parity before the end"). For beginner you just solve 1 single piece piece instead of 2. For intermediate and further you solve 3 pieces instead of 2 (with some added moves)

And the way you solve the final parity is different, but that doesn't happen with this scramble.

I think the limit for this method will be around 40 seconds (about 2 moves per second). I can do it in 60, Erik did it in 52 at the Chech Open and has improved a lot since then.

Just remember, don't look at the pieces you are solving, always look for the next center-edge. If you do it correctly you don't stop at all during the 24 semi-pairs and you have only looked at the Front-Left-Down Edge-Wing once!

[Mike Hughey]

Sorry I didn't reply sooner, Arnaud! I hadn't had the chance to actually try out your examples to see how they went.

Thank you very much for this - it comforted me by satisfying me that I'm doing it right - my solution would have looked very much like your Advanced one, except for the fact that I would have gone wrong on the very first move by setting up with F D' F' instead. I have everything else optimized by turning the cube, but somehow I missed this one. (I would even get it right if it was on the other side - funny how you develop blind spots for things like this!) So that might help me a little.

One thing I wonder about: If you have a case of pairs of what BigCubes.com calls the "double edge flip", do you have any simpler way of solving them other than to do the algorithm they have there? For that matter, I guess just a "single edge flip" could happen as well. If I ever encounter that (which happens often enough I've had it a number of times - once even with 2 pairs in a single solve!), I just perform that algorithm when I get to the end. But I was wondering if there's a better way that you know of.

[AvGalen]

"double edge flip" and "single edge flip" are extremely rare. Basically they will only occur if they were already there after doing centers. They will never be formed during the edge-pairing as long as you keep using a semi-pair as your starting position.

If they do happen to occur, fix them directly at the beginning of the edge-pairing phase with the following moves:

Single edge flip:
* Put the wrong edge at the Front-Right (mostly without a move by using cube rotations)
* Make sure the Front-Left doesn't have a semi-pair (that is why you should do this as soon as possible. Most of the time there isn't a semi-pair at Front-Left or an L or L' move will do)
* Just do what you would do in (special case "flipped wing") with two added double layer u turns so d (F' U2 F) (R U R') d' becomes d u' (F' U2 F) (R U R') u d'
* You have used 10 moves for 2 semi-pairs

Double edge flip:
* Put the wrong edge at the Front-Right (mostly without a move by using cube rotations)
* Make sure the Front-Left has the other wrong edge (2 moves at most)
* Just do what you would do in (special case "flipped wing") with two added double layer u turns so d (F' U2 F) (R U R') d' becomes d u' (F' U2 F) (R U R') u d'
* You have used 10-12 moves for 4 semi-pairs

Yes, that's right it's the same!

[Mike Hughey]

Okay, Arnaud! Thanks! I see that for the "double edge flip", this really isn't any different from doing the BigCubes.com solution, but for the "single edge flip", this is a real savings, so that's helpful. The only problem I see with it is that I would think it would be easy to not notice that one of these is around when starting the edges, and since it's so rare, it doesn't seem worthwhile to actually look for it. But I guess the idea should be that, as soon as you spot one, you can stop what you're doing, fix that, and then go back to what you were doing.

Yes, I know those are extremely rare, but believe it or not I actually had a solve once where I was using your method and I had 4 of them (2 "double edge flips") in the same solve. I couldn't believe my bad luck. But I see now that it's not really all that big of a deal.